Problem: Reduce to lowest terms: $- \dfrac{1}{2} \div \dfrac{1}{8} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{1}{8}$ is $ \dfrac{8}{1}$ Therefore: $ - \dfrac{1}{2} \div \dfrac{1}{8} = - \dfrac{1}{2} \times \dfrac{8}{1} $ $ \phantom{- \dfrac{1}{2} \times \dfrac{8}{1}} = \dfrac{-1 \times 8}{2 \times 1} $ $ \phantom{- \dfrac{1}{2} \times \dfrac{8}{1}} = \dfrac{-8}{2} $ The numerator and denominator have a common divisor of $2$, so we can simplify: $ \dfrac{-8}{2} = \dfrac{-8 \div 2}{2 \div 2} = -4 $